Interval Estimation Method Research Articles

ICPUTRD: Image Cloud Platform for use in tagging and research on decomposition.

Human decomposition studies aim to understand the various factors influencing human decay to assess the deceased and develop postmortem interval (PMI) estimation methods. These types of studies are typically conducted through physical experiments examining the deceased; however, big data systems have the potential to transform how large-scale forensic anthropology research questions can be addressed with curated images of donors with known demographic, climatic, and postmortem historical data. This study introduces ICPUTRD (Image Cloud Platform for Use in Tagging and Research on Decomposition), a web-based software system, which enables forensic scientists to easily access, enhance (or curate), and analyze very large photographic collections documenting the longitudinal process of human decomposition. ICPUTRD, a JavaScript-based application, was designed and built through a combination of the Waterfall and Agile software development life-cycle methods and provides an image search and tagging features with a predefined nomenclature of forensic-related keywords. To evaluate the system, a user study was conducted, involving 27 participants who completed pre- and post-study surveys and three research tasks. Analysis of the study results confirmed the feasibility and practicality of ICPUTRD to facilitate aspects of forensic research and casework involving large collections of digital photographs of human decomposition. It was observed that the nomenclature lacked certain law enforcement keywords, so future work will focus on expanding it to ensure ICPUTRD is suited for all its intended users.

Nonparametric bootstrap methods for interval estimation of the area under the ROC curve with correlated diagnostic test data: application to whole-virus ELISA testing in swine.

Developing and evaluating novel diagnostic assays are crucial components of contemporary diagnostic research. The receiver operating characteristic (ROC) curve and the area under the ROC curve (AUC) are frequently used to evaluate diagnostic assays' performance. The variation in AUC estimation can be quantified nonparametrically using resampling methods, such as bootstrapping, and then used to construct interval estimation for the AUC. When multiple observations are observed from the same subject, which is very common in veterinary diagnostic tests evaluation experiments, a traditional bootstrap-based method can fail to provide valid interval estimations of AUC. In particular, the traditional method does not account for the correlation among data observations and could result in interval estimation that fails to cover the true AUC adequately at the desired confidence level. In this paper, we proposed two novel methods to calculate the confidence interval of the AUC for correlated diagnostic test data based on cluster bootstrapping and hierarchical bootstrapping, respectively. Our simulation studies showed that both proposed methods had adequate coverage probabilities which were higher than the existing traditional method when there were intra-subject correlations. We also discussed applying the proposed methods to evaluate a novel whole-virus ELISA (wv-ELISA) diagnostic assay in detecting porcine parainfluenza virus type-1 antibodies in swine serum.

Accelerated degradation data analysis based on inverse Gaussian process with unit heterogeneity

The unit heterogeneity of products and the nonlinear parameter-stress relationship often exist in practice. Therefore, considering the unit heterogeneity, the nonlinear accelerated model and inverse Gaussian process are developed to depict the accelerated degradation data. On the other hand, this more realistic model leads a challenge to derive the model parameter interval estimation. Thereby, a novel two-step interval estimation method is proposed for the proposed accelerated degradation model. First, generalized confidence intervals of the parameters characterizing random effect are derived from the Cornish–Fisher expansion, and their cumulative distribution functions are obtained. Then, using the generalized pivotal quantity procedure, generalized confidence intervals of the accelerated model parameters are derived. In addition, generalized confidence intervals of predictive reliability indexes are derived to guide the practical application. Finally, simulation studies and two real examples on Spiral springs and integrated circuit devices are presented to demonstrate the implementation of the proposed method.

Reliability Estimation of Retraction Mechanism Kinematic Accuracy under Small Sample

Due to intricate operating conditions, including structural clearances and assembly deviations, the acquisition of test data of landing gear retraction mechanism is limited, posing challenges for reliability analysis. To solve the problem, a Bayesian-based reliability analysis method by fusing prior and test data is proposed, focusing on the mechanism kinematic accuracy under small-sample conditions. Firstly, a dynamic simulation model is established to collect prior data, and retraction tests are conducted to obtain test data. Then, based on Bayesian theory, the motion accuracy parameter estimation model integrating prior and test samples is established. To obtain accurate hyper parameters, the prior samples are expanded using neural network. Finally, taking the retraction mechanism as the research object, the kinematic accuracy reliability is quantified, and the impact of uncertainty factors is analyzed in depth. The results show that the proposed method is superior to the classical interval estimation method in stability and effectively mitigates the impact of uncertainty factors.

Bayesian and likelihood estimation of multicomponent stress–strength reliability from power Lindley distribution based on progressively censored samples

In this article, the problem of estimation of reliability of a ℓ-component system when both the stress and strength components are assumed to have a power Lindley distribution is discussed. The multicomponent stress–strength reliability parameter is obtained using both the Bayesian and the classical approaches when component-wise each unit follows a power Lindley distribution. To estimate the multicomponent stress–strength reliability parameter under the classical approach, the method of maximum likelihood and the asymptotic confidence interval estimation method are used as point and interval estimation methods, respectively. Under the Bayesian paradigm, the reliability parameter is estimated under the linear exponential loss function using the Lindley approximation, the Tierney–Kadane approximation and the Markov chain Monte Carlo (MCMC) techniques and subsequently highest posterior density credible intervals are obtained. To validate the efficacy of the proposed estimation strategies, a simulation study is carried out. Finally, two real-life data sets are re-analysed for illustrative purposes.

Statistical inference in Burr type XII lifetime model based on progressive randomly censored data

Censoring commonly occurs in real-world scenarios, either intentionally or unintentionally. Unintentional (or accidental) censoring usually happens randomly, i.e., it is out of the experimenters’ control, such as broken equipment, lack of follow-up, etc. Experimenters typically use intentional censoring to save experimental time and cost. In this article, we develop frequentist and Bayesian statistical inferential procedures for the parameters and reliability characteristics of the Burr type XII lifetime model under the Koziol-Green model based on progressive randomly censored data. For the frequentist approach, maximum likelihood methods for point and interval estimation are developed. For the Bayesian approach, the Bayes estimates under the squared error loss function (SELF) are evaluated using the Markov Chain Monte Carlo (MCMC) and Tierney-Kadane (T-K) approximation techniques. A Monte Carlo simulation study is used to assess the performance of the proposed estimation procedures. A real data analysis is performed to illustrate the proposed methods. Moreover, obtaining progressive censoring schemes for experimental planning purposes is also discussed.

HIE-EDT: Hierarchical interval estimation-based evidential decision tree

Decision tree algorithm, because of its strong interpretability and high algorithm efficiency, is widely used in the field of pattern recognition and classification. When the number of data samples is small and there is uncertainty in the data, it is difficult for the traditional decision tree algorithm to fully mine the effective information in the data. In this paper, we use the Dempster–Shafer framework to model data uncertainty and propose a hierarchical interval estimation method to improve decision tree algorithms. The proposed method constructs intervals through two methods of attribute boundary and mean square error estimation, which not only utilizes the characteristics of intervals to model the inaccuracy of data, but also constrains intervals from two aspects, narrowing the representation range of available information. By comparing with the classic decision tree algorithm and the decision tree algorithm based on single interval estimation, the proposed method can perform classification tasks robustly and accurately in different types of data under seven data sets.

Unsupervised machine learning method for indirect estimation of reference intervals for chronic kidney disease in the Puerto Rican population

Reference intervals (RIs) for clinical laboratory values are extremely important for diagnostics and treatment of patients. However, the determination of these ranges is costly and time-consuming. As a result, often different unverified RIs are used in practice for the same analyte and the same range is used for all patients despite evidence that the values are gender, age, and ethnicity dependent. Moreover, the abnormal flags are rudimentary, merely indicating if a value is within the RI. At the same time, clinical lab data generated in the everyday medical practice contains a wealth of information, that given the correct methodology, can help determine the RIs for each specific segment of the population, including populations that suffer from health disparities. In this work, we develop unsupervised machine learning methods, based on Gaussian mixtures, to determine RIs of analytes related to chronic kidney disease, using millions of routine lab results for the Puerto Rican population. We show that the measures are both gender and age dependent and we find evidence for normal age-related organ function deterioration and failure. We also show that the joint distribution of measures improves the diagnostic value of the lab results.

Estimation of turnout irregularities using vehicle responses with improved BiLSTM and Gaussian process regression

Railway turnout irregularities pose a safety risk, but existing detection methods using expensive trains with inertial navigation systems and laser measurement devices are cost-prohibitive and time-consuming for high-speed railways. This paper proposes a low-cost and real-time solution for estimating railway turnout irregularities using vehicle body acceleration, allowing for continuous monitoring of dynamic changes. A Bayesian-optimized improved bidirectional long short-term memory neural network model (BO-BiLSTM) was proposed in this paper, utilizing the vehicle's vertical and lateral acceleration as input to achieve point estimation of irregularities, with an estimation error approximately 50% lower than that of traditional recurrent neural networks. In addition, an interval estimation model combining BO-BiLSTM and Gaussian process regression (BO-BiLSTM-GPR) was proposed. Compared to the traditional interval estimation method Bootstrap, under the condition of narrow interval width, GPR ensures that over 90% of the measured values fall within the estimated interval and provides a better solution to the trade-off between interval estimation reliability and uncertainty.

Expression of human cardiac-specific genes: a novel method for post-mortem interval estimation.

In legal medicine, the determination of post-mortem interval (PMI) is not only an important but also one of the most difficult aspects. Several methods are used to estimate PMI such as physicochemical, entomological, biochemical, metabolic, autolytic, and physical methods. These methods provide a wide range of PMI as they are affected by different factors. The approach behind the present study is to calculate an accurate PMI by using mRNA degradation and fold change expression (FCE) of cardiac-specific genes viz. N-terminal pro-B-type natriuretic peptide (NPPB) and cardiac troponin I (TNNI3). Seventeen cadaver heart tissues were analysed within a time frame of up to 12 hours from the time since death, at different time intervals at room temperature. Gene expression was determined and the data were analysed using the value of average delta Ct (ΔCt) value of the assessed gene and housekeeping gene. Delta delta Ct (ΔΔCt) method was used to calculate the FCE at the different 7-time groups. The FCE of TNNI3 was almost stable till 15 hours of PMI and then after 15 hours, expression shows a decrease up to 24 hours after death; whereas, NPPB shows that FCE was stable till 12 hours of PMI and then after 12 hours, expression shows a decrease up to 24 hours after death. The FCE of NPPB and TNNI3 was almost stable till 12 hours. Thus, the estimation of PMI by analysis of the FCE of cardiac-specific genes can be a new promising method in forensic medicine.

Secure iterative interval estimation method for cyber-physical systems subject to stealthy deception attacks

This paper studies a secure iterative interval estimation approach for cyber-physical systems subject to stealthy deception attacks. Under the hypothesis that the system is accessed by a stealthy attack, an iteration scheme integrating the T-N-L observer framework is employed to reconstruct the system state. With the help of a structure separation method, a sufficient condition in terms of linear matrix inequality is provided to obtain convergent observation errors under deception attacks. Resorting to the reachability analysis, a secure state interval is built by means of the analyzed attack bounds and the observation error interval. Simulation studies verify the effectiveness of the proposed method for attack and attack-free cases.

Wearable Integrated Online Fusion Learning Filter for Heart PPG Sensing Tracking

Heart rate is an important physiological indicator of the human body. It can evaluate the activity of the heart and the degree of fatigue. It can be further used to assess emotions by monitoring heart rate changes and voice recording or breathing. Single-lead or multi-lead equipment is often used to monitor ECG in medical treatment. However, it brings inconvenience to daily life to record the heart rate from a free-living natural environment. Due to the subject’s voluntary or involuntary movement, it is difficult to collect ideal photoplethysmography (PPG) signal by using wearable device as it is continually interfered by the motion artifacts (MA). These MAs seriously affect the calculation and online monitoring of the heart rate. This paper proposes a wearable device with real-time online fusion learning for heart PPG tracking. In particular, it proposes a Recursive Least Squares algorithm to fuse three-axis acceleration signals to remove motion artifacts from PPG signals. In order to further determine the heart rate frequency range and select the appropriate spectrum peak, a decision tree spectrum interval estimation method is proposed to provide prior information for PPG signal spectrum tracking, so as to optimize the spectrum peak estimation. The performance of the proposed device, which is an integrated internet of things with wearable platform, has been shown to be robust to natural and unpredictable situations. Experimental results have confirmed that the proposed method can adaptively track the PPG signal with high accuracy.

The Euler–Riemann [formula omitted] function and the estimation of the power-law exponent

Power-law distributions are widely used in statistical analysis of extreme events and complex systems. For the commonly used power-law distributions, the variances do not exist. This makes the error analysis of point estimation and the construction of interval estimation of exponent parameter more difficult. Based on Euler product formula, this paper gives a summation formula of derivative of logarithmic Riemann ζ function and provides a more convenient method for calculating maximum likelihood estimation. By compressed transformation, the variance is ensured to be finite and the maximum likelihood estimation of the exponent is equivalent to its moment estimation. So a method of interval estimation based on the central limit theorem is proposed. In addition, this paper also gives an interval estimation method based on the acceptance domain of likelihood ratio test. The advantages of the proposed methods are showed in synthetic power-law data and illustrated with applications in a set of empirical data.

A double-Cox model for non-proportional hazards survival analysis with frailty.

The Cox regression, a semi-parametric method of survival analysis, is extremely popular in biomedical applications. The proportional hazards assumption is a key requirement in the Cox model. To accommodate non-proportional hazards, we propose to parameterize the shape parameter of the baseline hazard function using the additional, separate Cox-regression term which depends on the vector of the covariates. This parametrization retains the general form of the hazard function over the strata and is similar to one in Devarajan and Ebrahimi (Comput Stat Data Anal. 2011;55:667-676) in the case of the Weibull distribution, but differs for other hazard functions. We call this model the double-Cox model. We formally introduce the double-Cox model with shared frailty and investigate, by simulation, the estimation bias and the coverage of the proposed point and interval estimation methods for the Gompertz and the Weibull baseline hazards. For real-life applications with low frailty variance and a large number of clusters, the marginal likelihood estimation is almost unbiased and the profile likelihood-based confidence intervals provide good coverage for all model parameters. We also compare the results from the over-parametrized double-Cox model to those from the standard Cox model with frailty in the case of the scale-only proportional hazards. The model is illustrated on an example of the survival after a diagnosis of type 2 diabetes mellitus. The R programs for fitting the double-Cox model are available on Github.

Interval estimation for discrete-time linear time-delay systems based on state augmentation

This paper investigates an interval estimation method for discrete-time linear time-delay systems subject to unknown but bounded disturbances and noise. We utilize the state augmentation technique to decouple the time delays. The interval estimation problem for the time-delay system will be transformed into that for a delay-free state augmented system. We then propose a two-step method which consists of robust observer design and zonotope-based interval analysis to achieve interval estimation. In observer design, a T−N−L observer is used to provide more degrees of design freedom, whose robustness is characterized by H∞ performance. Finally, a numerical example is provided to demonstrate the effectiveness and superiority of the proposed method.

Theoretical Analysis and Numerical Simulation of the Motion of RDX Deflagration-Driven Flyer Plate Based on Laser-Initiated Micro-Pyrotechnic Devices.

Miniaturized laser-initiated pyrotechnic devices have great application prospects in aerospace and modern weapon systems due to their excellent energy output performance and reliability. In order to develop a low-energy insensitive laser detonation technology based on a two-stage charge structure, it is important to deeply analyze the motion law of a titanium flyer plate driven by the deflagration of the first-stage charge (RDX). The effects of the charge mass of RDX, flyer plate mass, and barrel length on the motion law of flyer plates were studied through a numerical simulation method based on the Powder Burn deflagration model. The consistency between the numerical simulation and the experimental results was analyzed using the paired t confidence interval estimation method. The results show that the Powder Burn deflagration model can effectively describe the motion process of the RDX deflagration-driven flyer plate with a 90% confidence level, and its velocity error is ≤6.7%. The speed of the flyer plate is proportional to the mass of the RDX charge, inversely proportional to the mass of the flyer plate, and exponentially related to its moving distance. As the moving distance of the flyer plate increases, the RDX deflagration products and air in front of the flyer plate are compressed, which inhibits the motion of the flyer plate. In the optimum state (the mass of the RDX charge is 60 mg, the mass of the flyer is 85 mg, and the length of the barrel is 3 mm), the speed of the titanium flyer reaches 583 m/s, and the peak pressure of the RDX deflagration reaches 2182 MPa. This work will provide a theoretical basis for the refined design of a new generation of miniaturized high-performance laser-initiated pyrotechnic devices.

Scientific progress in information theory quantifiers

The Bandt and Pompe method (BPM) has been successfully applied to estimate the information theory quantifiers. The most significant limitation of the BPM is that this approach is based on point estimation. This research provides scientific progress into the several applications of the information theory quantifiers. In this way, we propose a new statistic confidence interval estimation method for the Permutation Entropy, Fisher Information Measure, and Macroeconophysics Indicator of Efficiency (MIEE). Therefore, we examine quarterly Gross Domestic Product (GDP) time series for 25 countries members of the Organization for Economic Co-operation and Development (OECD). The periods cover more than 59 years, from Q1-1960 to Q3-2019, with 238 data points. For each GDP time series, we employ the non-parametric method Local Block Bootstrap to provide a stylized fact about an empirical distribution for these data taking into account the information theory quantifiers. Based on the values of the empirical distribution of the information theory quantifiers, we construct the Shannon-Fisher causality plane (SFCP), which allows us to quantify the disorder and evaluate randomness present in the time series of quarterly GDP in each country. In addition, we use information theory quantifiers to rank the most efficient countries in allocating the resources arising from economic growth to generate a virtuous cycle of growth. Also, we apply the Principal Component Analysis (PCA) to check the results of the empirical distribution of the MIEE. We find the PCA promotes the same result as the MIEE. Our results suggest an alternative form of clustering using information theory quantifiers linked to the similarity of countries’ GDPs and the mutual influences of one country’s economic growth on the others.

Prediction interval estimation of sinter drum index based on light gradient boosting machine and kernel density estimation

ABSTRACT Owing to the uncertainty operation in the sintering process, it is easy to produce uncertain prediction errors in the single drum index prediction model, which makes the prediction results lack certain reliability. Accurate and reliable prediction of the drum index can help improve the drum index. In this paper, a prediction interval estimation method of drum index based on a light gradient boosting machine (LightGBM) and kernel density estimation (KDE) is proposed. LightGBM can obtain accurate points prediction of drum index, and then use the KDE method to obtain the estimated prediction interval of drum index. The comparison results of different methods show that LightGBM has high prediction performance, and KDE can well quantify the prediction error of drum index, which verifies the effectiveness of the prediction interval estimation method combined with LightGBM and KDE, and provides more reliable decision-making information for the optimisation of sintering process parameters.

Probabilistic seismic performance assessment of nuclear containment structure considering statistical uncertainty

Statistical uncertainty is inherently involved in probabilistic seismic performance assessment of containment structure due to heavy computational efforts of nonlinear dynamic analysis. Aiming at the statistical uncertainty involved in seismic fragility and seismic risk evaluation of containment structure, this study proposes a method for quantifying the statistical uncertainty in probabilistic seismic performance assessment of the containment structure. Taking a three story reinforced concrete frame as an example, effectiveness and efficiency of the proposed method for confidence interval estimation of seismic fragility curve is verified. Then, the proposed method is applied to fragility analysis and seismic risk evaluation of the containment structure. Roof drift of the containment structure under different ground motion intensity levels is discussed. Confidence interval for seismic fragility curve and seismic risk of the containment structure considering statistical uncertainty is quantified by the proposed method. The results highlighted the necessity for quantifying the impact of statistical uncertainty involved in probabilistic seismic performance evaluation of the containment structure.

Assessing standardized contrast effects in ANCOVA: Confidence intervals, precision evaluations, and sample size requirements.

Standardized effect sizes and confidence intervals are useful statistical assessments for comparing results across different studies when measurement units are not directly comparable. This paper aims to describe and compare confidence interval estimation methods for the standardized contrasts of treatment effects in ANCOVA designs. Sample size procedures are also presented to assure that the resulting confidence intervals yield informative estimation with adequate precision. Exact interval estimation approach has theoretical and empirical advantages in coverage probability and interval width over the approximate interval procedures. Numerical investigations of the existing method reveal that the omission of covariate variables has a negative impact on sample size calculations for precise interval estimation, especially when there is disparity in influential covariate variables. The proposed approaches and developed computer programs fully utilize covariate properties in interval estimation and provide accurate sample size determinations under the precision considerations of the expected interval width and the assurance probability of interval width.